6. Let (f=left{left(x,frac{x^2}{1+x^2}right):mathrm{ x} in Rright}) be a function from R into R. Determine the range of f. Relations and Functions Miscellaneous Exercise Previous Next Class 11 Relations and Functions Miscellaneous Exercise 1. The relation f is defined by (f(x)={begin{matrix}x^2,mathrm{ 0}…
5. Find the domain and the range of the real function f defined by (f(x)=left|x-1right|). Relations and Functions Miscellaneous Exercise Previous Next Class 11 Relations and Functions Miscellaneous Exercise 1. The relation f is defined by (f(x)={begin{matrix}x^2,mathrm{ 0} le xle3\3x,mathrm{ 3}le…
4. Find the domain and the range of the real function f defined by (fleft(xright)=sqrt{x-1}). Relations and Functions Miscellaneous Exercise Previous Next Class 11 Relations and Functions Miscellaneous Exercise 1. The relation f is defined by (f(x)={begin{matrix}x^2,mathrm{ 0} le xle3\3x,mathrm{ 3}le…
3. Find the domain of the function (fleft(xright)=frac{x^2+2x+1}{x^2-8x+12}). Relations and Functions Miscellaneous Exercise Previous Next Class 11 Relations and Functions Miscellaneous Exercise 1. The relation f is defined by (f(x)={begin{matrix}x^2,mathrm{ 0} le xle3\3x,mathrm{ 3}le xlemathrm{10}\end{matrix}) (g(x)={begin{matrix}x^2,mathrm{ 0} le xle2\3x,mathrm{ 2}le xlemathrm{10}\end{matrix})…
1. The relation f is defined by (f(x)={begin{matrix}x^2,mathrm{ 0} le xle3\3x,mathrm{ 3}le xlemathrm{10}\end{matrix}) (g(x)={begin{matrix}x^2,mathrm{ 0} le xle2\3x,mathrm{ 2}le xlemathrm{10}\end{matrix}) Show that f is a function and g is not a function. Relations and Functions Miscellaneous Exercise Previous Next Class 11…
2. If (f(x)=x^2), find (frac{f(1.1)-f(1)}{(1.1-1)}). Relations and Functions Miscellaneous Exercise Previous Next Class 11 Relations and Functions Miscellaneous Exercise 1. The relation f is defined by (f(x)={begin{matrix}x^2,mathrm{ 0} le xle3\3x,mathrm{ 3}le xlemathrm{10}\end{matrix}) (g(x)={begin{matrix}x^2,mathrm{ 0} le xle2\3x,mathrm{ 2}le xlemathrm{10}\end{matrix}) Show that f…
10. Find sets A, B and C such that A∩B, B∩C and A∩C are non-empty sets and A∩B∩C=(phi). Sets Miscellaneous Exercise Previous Next Class 11 Sets Miscellaneous Exercise 1. Decide, among the following sets, which sets are subsets of one and…
9. Let A and B be sets. If A∩X=B∩X=(phi) and A∪X=B∪X for some set X, show that A=B. (Hints A=A∩(A∪X), B=B∩(B∪X) and use Distributive law) Sets Miscellaneous Exercise Previous Next Class 11 Sets Miscellaneous Exercise 1. Decide, among the following sets,…
8. Show that A∩B=A∩C need not imply B=C. Sets Miscellaneous Exercise Previous Next Class 11 Sets Miscellaneous Exercise 1. Decide, among the following sets, which sets are subsets of one and another: A={x : x∈R and x satisfy x2–8x+12=0}, B={2,4,6}, C={2,4,6,8,…
7. Using properties of sets, show that (i) A∪(A∩B)=A (ii) A∩(A∪B)=A. Sets Miscellaneous Exercise Previous Next Class 11 Sets Miscellaneous Exercise 1. Decide, among the following sets, which sets are subsets of one and another: A={x : x∈R and x…
